On the basis of this microscopic formulation, in the long-wavelength limit, we propose a noncommutative field-theoretical description, which in a commutative limit reproduces the Son's theory, with additional terms that may be expected on physical grounds. We also discuss pairing instabilities within the developed microscopic framework, and provide a physical understanding of the
\(p\) -wave pairing instability in the LLL, and in the sLL. The pairing in the LLL is of the BCS, weak-coupling
kind, and this may explain the scarcity of the pairing phenomena in the LLL. On the other hand, the pairing
in the sLL is of the strong coupling (weak pairing) kind as proposed and discussed in [1]},
though we find that the Dirac CF band dispersion, \(\epsilon (k)\) , is flatter: it obeys a third-power law, i.e.,
\(\epsilon (k)\sim k^3\) .
